Spatial Regression
Jason Edelkind
2023-11-16
OLS Model
##
## Call:
## lm(formula = equation, data = fl_pov)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.211930 -0.063175 -0.007283 0.051057 0.276869
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.185293 0.622157 -1.905 0.06241 .
## rural 0.153878 0.258799 0.595 0.55475
## urban 0.083299 0.051566 1.615 0.11240
## lnmanufacturing 0.092756 0.034704 2.673 0.01008 *
## lnag 0.040325 0.023152 1.742 0.08758 .
## lnretail 0.276450 0.080755 3.423 0.00123 **
## lnhealthss 0.363312 0.105548 3.442 0.00116 **
## lnconstruction 0.077380 0.067385 1.148 0.25620
## lnlesshs 0.173800 0.081454 2.134 0.03770 *
## lnsinglemom -0.057206 0.076525 -0.748 0.45817
## lnblack 0.007684 0.035991 0.213 0.83179
## lnhispanic 0.047137 0.040613 1.161 0.25119
## lnuninsured 0.092831 0.187230 0.496 0.62216
## lnincome_ratio -0.150950 0.150096 -1.006 0.31931
## lnteenbirth 0.032004 0.039240 0.816 0.41852
## lnunmarried 0.093013 0.061724 1.507 0.13800
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.1125 on 51 degrees of freedom
## Multiple R-squared: 0.6659, Adjusted R-squared: 0.5676
## F-statistic: 6.776 on 15 and 51 DF, p-value: 0.0000001045The OLS model includes several significant predictor variables including lnhealthss,lnretail,lnmanufacturing, lnlesshs
Visreg OLS Plots
Moran’s Correlation Test for Spatial Dependency
lm.morantest(ols, cont.neighb)##
## Global Moran I for regression residuals
##
## data:
## model: lm(formula = equation, data = fl_pov)
## weights: cont.neighb
##
## Moran I statistic standard deviate = 2.3231, p-value = 0.01009
## alternative hypothesis: greater
## sample estimates:
## Observed Moran I Expectation Variance
## 0.134745905 -0.046940024 0.006116573P-value=.01009. Spatial dependency detected in the dataset, reject null hypothesis (no spatial correlation in residuals)
LaGrange Multiplier Test
lm.LMtests(ols, cont.neighb, test="all")##
## Lagrange multiplier diagnostics for spatial dependence
##
## data:
## model: lm(formula = equation, data = fl_pov)
## weights: cont.neighb
##
## LMerr = 2.5538, df = 1, p-value = 0.11
##
##
## Lagrange multiplier diagnostics for spatial dependence
##
## data:
## model: lm(formula = equation, data = fl_pov)
## weights: cont.neighb
##
## LMlag = 2.5152, df = 1, p-value = 0.1128
##
##
## Lagrange multiplier diagnostics for spatial dependence
##
## data:
## model: lm(formula = equation, data = fl_pov)
## weights: cont.neighb
##
## RLMerr = 0.25252, df = 1, p-value = 0.6153
##
##
## Lagrange multiplier diagnostics for spatial dependence
##
## data:
## model: lm(formula = equation, data = fl_pov)
## weights: cont.neighb
##
## RLMlag = 0.21392, df = 1, p-value = 0.6437
##
##
## Lagrange multiplier diagnostics for spatial dependence
##
## data:
## model: lm(formula = equation, data = fl_pov)
## weights: cont.neighb
##
## SARMA = 2.7677, df = 2, p-value = 0.2506LMerr=0.1100
LMlag=0.1128
RLMerr=0.6153
RLMlag=0.6437
SARMA= 0.2506
Spatial error or spatial lag model would be best.
Spatially Lagged X Model
SLX.model <- spatialreg::lmSLX(equation, data=fl_pov, cont.neighb)
summary(SLX.model)##
## Call:
## lm(formula = formula(paste("y ~ ", paste(colnames(x)[-1], collapse = "+"))),
## data = as.data.frame(x), weights = weights)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.161625 -0.042118 -0.000216 0.048149 0.182283
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -3.80184 2.00676 -1.895 0.066212 .
## rural 0.22298 0.29174 0.764 0.449662
## urban 0.11494 0.05771 1.992 0.054016 .
## lnmanufacturing 0.12268 0.03812 3.218 0.002728 **
## lnag 0.05156 0.02218 2.325 0.025821 *
## lnretail 0.30018 0.07594 3.953 0.000346 ***
## lnhealthss 0.33824 0.11627 2.909 0.006176 **
## lnconstruction 0.03111 0.07117 0.437 0.664591
## lnlesshs 0.24696 0.07955 3.105 0.003702 **
## lnsinglemom -0.05593 0.08605 -0.650 0.519797
## lnblack 0.04431 0.03775 1.174 0.248207
## lnhispanic -0.01840 0.05123 -0.359 0.721581
## lnuninsured 0.07605 0.20763 0.366 0.716302
## lnincome_ratio 0.02867 0.15803 0.181 0.857044
## lnteenbirth 0.06476 0.04093 1.582 0.122372
## lnunmarried 0.13189 0.06962 1.894 0.066228 .
## lag.rural 1.15152 0.51489 2.236 0.031611 *
## lag.urban 0.33223 0.12356 2.689 0.010796 *
## lag.lnmanufacturing 0.10188 0.09464 1.076 0.288874
## lag.lnag 0.09856 0.04809 2.049 0.047756 *
## lag.lnretail 0.22230 0.20212 1.100 0.278705
## lag.lnhealthss -0.36290 0.26199 -1.385 0.174527
## lag.lnconstruction -0.00185 0.19276 -0.010 0.992397
## lag.lnlesshs -0.43914 0.19831 -2.214 0.033223 *
## lag.lnsinglemom 0.12321 0.20901 0.589 0.559216
## lag.lnblack -0.04880 0.09097 -0.536 0.594918
## lag.lnhispanic -0.07987 0.10571 -0.756 0.454846
## lag.lnuninsured 0.30868 0.51728 0.597 0.554413
## lag.lnincome_ratio 0.42511 0.36337 1.170 0.249724
## lag.lnteenbirth 0.08151 0.09217 0.884 0.382376
## lag.lnunmarried 0.39688 0.11878 3.341 0.001953 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.09507 on 36 degrees of freedom
## Multiple R-squared: 0.8316, Adjusted R-squared: 0.6912
## F-statistic: 5.924 on 30 and 36 DF, p-value: 0.0000004974It looks like some of the lag variables are significant
summary(spatialreg::impacts(SLX.model, cont.neighb), zstats = TRUE)[["pzmat"]]## Direct Indirect Total
## rural 0.4446806472 0.0253236263 0.0200477943
## urban 0.0463883266 0.0071718323 0.0029606849
## lnmanufacturing 0.0012890520 0.2817126630 0.0261975419
## lnag 0.0200684510 0.0404154964 0.0027134722
## lnretail 0.0000772833 0.2714045632 0.0211018050
## lnhealthss 0.0036239322 0.1660029939 0.9215749866
## lnconstruction 0.6619797355 0.9923437214 0.8964755149
## lnlesshs 0.0019056880 0.0268041254 0.3742232689
## lnsinglemom 0.5156703661 0.5555340302 0.7741950207
## lnblack 0.2405003865 0.5916181336 0.9662263740
## lnhispanic 0.7194834523 0.4499312276 0.3563418815
## lnuninsured 0.7141585725 0.5506780765 0.4869107567
## lnincome_ratio 0.8560258964 0.2420366067 0.2790049845
## lnteenbirth 0.1136252026 0.3765077581 0.1899708337
## lnunmarried 0.0581722443 0.0008340691 0.0002792914Significant variables in analysis include rural, urban, lnmanufacturing, lnag, lnretail, lnunmarried
Spatial Lag Model
sp.lag.model <- spatialreg::lagsarlm(equation, data=fl_pov, cont.neighb)
summary(sp.lag.model, Nagelkerke = TRUE)##
## Call:
## spatialreg::lagsarlm(formula = equation, data = fl_pov, listw = cont.neighb)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.1941231 -0.0638849 -0.0074391 0.0404584 0.2835548
##
## Type: lag
## Coefficients: (asymptotic standard errors)
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -1.543273 0.555321 -2.7791 0.0054516
## rural 0.077834 0.219494 0.3546 0.7228847
## urban 0.088421 0.044629 1.9812 0.0475643
## lnmanufacturing 0.091538 0.029419 3.1116 0.0018610
## lnag 0.037578 0.019633 1.9140 0.0556178
## lnretail 0.255516 0.068874 3.7099 0.0002073
## lnhealthss 0.318512 0.092958 3.4264 0.0006116
## lnconstruction 0.083052 0.057243 1.4509 0.1468185
## lnlesshs 0.192075 0.069031 2.7825 0.0053948
## lnsinglemom -0.034916 0.066575 -0.5245 0.5999596
## lnblack 0.014295 0.030597 0.4672 0.6403558
## lnhispanic 0.033636 0.035046 0.9598 0.3371774
## lnuninsured 0.069739 0.159868 0.4362 0.6626694
## lnincome_ratio -0.114425 0.128014 -0.8938 0.3714042
## lnteenbirth 0.037512 0.033414 1.1226 0.2615867
## lnunmarried 0.074536 0.052358 1.4236 0.1545655
##
## Rho: 0.25587, LR test value: 2.8514, p-value: 0.091292
## Asymptotic standard error: 0.13205
## z-value: 1.9376, p-value: 0.052667
## Wald statistic: 3.7545, p-value: 0.052667
##
## Log likelihood: 61.87941 for lag model
## ML residual variance (sigma squared): 0.0090882, (sigma: 0.095332)
## Nagelkerke pseudo-R-squared: 0.6798
## Number of observations: 67
## Number of parameters estimated: 18
## AIC: -87.759, (AIC for lm: -86.907)
## LM test for residual autocorrelation
## test value: 1.525, p-value: 0.21687P=.091292, model is not significant. Spatial lag model not appropriate?
summary(spatialreg::impacts(sp.lag.model, listw = cont.neighb, R=100), zstats = TRUE)[["pzmat"]]## Direct Indirect Total
## rural 0.8588070657 0.8940939 0.863766360
## urban 0.0399045027 0.3257214 0.082537864
## lnmanufacturing 0.0029798597 0.2454009 0.012479823
## lnag 0.0500012937 0.3063356 0.082356281
## lnretail 0.0001572530 0.2365658 0.004436958
## lnhealthss 0.0003779642 0.1924958 0.001280392
## lnconstruction 0.1549220266 0.4010599 0.185042744
## lnlesshs 0.0029231991 0.2511549 0.012441264
## lnsinglemom 0.6476491850 0.8350248 0.687078732
## lnblack 0.6577398070 0.7037136 0.655939111
## lnhispanic 0.3689980179 0.6111192 0.402821009
## lnuninsured 0.6402059504 0.7533017 0.659254597
## lnincome_ratio 0.4110766736 0.5957018 0.438155159
## lnteenbirth 0.2146335575 0.4204202 0.250003750
## lnunmarried 0.2365760206 0.4067398 0.249166926P=.009. Significant variables include lnretail, lnhealthss, lnlesshs
Spatial Error Model
sp.err.model <- spatialreg::errorsarlm(equation, data=fl_pov, cont.neighb)
summary(sp.err.model, Nagelkerke = TRUE)##
## Call:
## spatialreg::errorsarlm(formula = equation, data = fl_pov, listw = cont.neighb)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.191807 -0.059441 -0.010568 0.055655 0.255013
##
## Type: error
## Coefficients: (asymptotic standard errors)
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -1.348885 0.533437 -2.5287 0.0114497
## rural -0.125390 0.208385 -0.6017 0.5473568
## urban 0.031479 0.039545 0.7960 0.4260154
## lnmanufacturing 0.090685 0.029166 3.1093 0.0018756
## lnag 0.022970 0.019106 1.2022 0.2292711
## lnretail 0.236081 0.061315 3.8503 0.0001180
## lnhealthss 0.386307 0.093113 4.1488 0.00003342
## lnconstruction 0.068321 0.051746 1.3203 0.1867314
## lnlesshs 0.233575 0.062175 3.7568 0.0001721
## lnsinglemom -0.088644 0.062287 -1.4232 0.1546910
## lnblack 0.026299 0.027717 0.9488 0.3427101
## lnhispanic 0.033171 0.037976 0.8735 0.3824008
## lnuninsured 0.199352 0.158989 1.2539 0.2098875
## lnincome_ratio -0.083870 0.116910 -0.7174 0.4731339
## lnteenbirth 0.026508 0.029111 0.9106 0.3625120
## lnunmarried 0.024901 0.048140 0.5173 0.6049679
##
## Lambda: 0.5859, LR test value: 6.7214, p-value: 0.0095261
## Asymptotic standard error: 0.11244
## z-value: 5.2108, p-value: 0.00000018803
## Wald statistic: 27.152, p-value: 0.00000018803
##
## Log likelihood: 63.8144 for error model
## ML residual variance (sigma squared): 0.0079102, (sigma: 0.088939)
## Nagelkerke pseudo-R-squared: 0.69777
## Number of observations: 67
## Number of parameters estimated: 18
## AIC: NA (not available for weighted model), (AIC for lm: -86.907)Significant variables include lnlesshs, lnretail, lnhealthss, lnmanufacturing
Comparing Contiguity Models
SLX R^2=0.6912
SLX
P=0.0000004974
Lag R^2=0.6798
Lag P=0.21687
Err R^2=0.698
Err P=.0095261
Appears that the spatially lagged X model is the best fit
Spatial Hausman Test of Error Model
This test will see if the results of the analysis verify the use of the selected model
spatialreg::Hausman.test(sp.err.model)##
## Spatial Hausman test (asymptotic)
##
## data: NULL
## Hausman test = 21.899, df = 16, p-value = 0.1465Based on the p value of 0.1465, we fail to reject null hypothesis that the estimation method should yield coefficients appropriate for a spatial error model. Spatial error model is appropriate.
Sadie Break
Nested Spatial Durbin Models
summary(sd.err, Nagelkerke = TRUE)##
## Call:
## spatialreg::errorsarlm(formula = equation, data = fl_pov, listw = cont.neighb,
## etype = "emixed")
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.1601513 -0.0416545 0.0016086 0.0440903 0.1699257
##
## Type: error
## Coefficients: (asymptotic standard errors)
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -3.48856169 1.48990406 -2.3415 0.0192081
## rural 0.11374914 0.19992266 0.5690 0.5693794
## urban 0.10892082 0.04217002 2.5829 0.0097975
## lnmanufacturing 0.12445530 0.02656529 4.6849 0.000002801185
## lnag 0.05692023 0.01528024 3.7251 0.0001952
## lnretail 0.33729957 0.05833540 5.7821 0.000000007379
## lnhealthss 0.35115281 0.07791564 4.5068 0.000006580234
## lnconstruction 0.03440683 0.05357488 0.6422 0.5207307
## lnlesshs 0.26539296 0.05983681 4.4353 0.000009195313
## lnsinglemom -0.07282453 0.06012351 -1.2112 0.2258000
## lnblack 0.04508305 0.02832751 1.5915 0.1114986
## lnhispanic 0.00086885 0.03360570 0.0259 0.9793735
## lnuninsured 0.03011682 0.14446658 0.2085 0.8348627
## lnincome_ratio 0.01791462 0.12211179 0.1467 0.8833635
## lnteenbirth 0.09143313 0.03111775 2.9383 0.0033002
## lnunmarried 0.10181182 0.04825709 2.1098 0.0348773
## lag.rural 1.04342564 0.38952971 2.6787 0.0073913
## lag.urban 0.33130202 0.09243425 3.5842 0.0003381
## lag.lnmanufacturing 0.08290062 0.06691287 1.2389 0.2153700
## lag.lnag 0.09488781 0.03732963 2.5419 0.0110255
## lag.lnretail 0.38790429 0.16016778 2.4219 0.0154412
## lag.lnhealthss -0.42582441 0.20168555 -2.1113 0.0347441
## lag.lnconstruction 0.01176520 0.14300478 0.0823 0.9344309
## lag.lnlesshs -0.34967744 0.15634211 -2.2366 0.0253114
## lag.lnsinglemom 0.12308154 0.17166633 0.7170 0.4733857
## lag.lnblack -0.06863803 0.07583983 -0.9050 0.3654446
## lag.lnhispanic -0.07482881 0.07463451 -1.0026 0.3160523
## lag.lnuninsured 0.03457217 0.36834813 0.0939 0.9252225
## lag.lnincome_ratio 0.41933819 0.29776982 1.4083 0.1590532
## lag.lnteenbirth 0.16284989 0.07724589 2.1082 0.0350136
## lag.lnunmarried 0.33491711 0.09556195 3.5047 0.0004571
##
## Lambda: 0.57034, LR test value: 5.3879, p-value: 0.020277
## Asymptotic standard error: 0.11513
## z-value: 4.9541, p-value: 0.00000072684
## Wald statistic: 24.543, p-value: 0.00000072684
##
## Log likelihood: 86.0926 for error model
## ML residual variance (sigma squared): 0.0040924, (sigma: 0.063972)
## Nagelkerke pseudo-R-squared: 0.84457
## Number of observations: 67
## Number of parameters estimated: 33
## AIC: NA (not available for weighted model), (AIC for lm: -102.8)R^2=0.84457, P=0,020277, error model looks appropriate
Impacts Matrix Analysis
summary(spatialreg::impacts(sd.err, listw = cont.neighb, R = 100), zstats = TRUE)[["pzmat"]]## Direct Indirect Total
## rural 0.569379410515021 0.0073912880 0.0191745521
## urban 0.009797452433238 0.0003381243 0.0002951369
## lnmanufacturing 0.000002801185230 0.2153699987 0.0087373887
## lnag 0.000195248381183 0.0110254894 0.0005331110
## lnretail 0.000000007378536 0.0154412036 0.0002367899
## lnhealthss 0.000006580234089 0.0347440970 0.7371823694
## lnconstruction 0.520730701109836 0.9344308963 0.7969056580
## lnlesshs 0.000009195313378 0.0253113758 0.6538144498
## lnsinglemom 0.225800046803441 0.4733856587 0.8063359597
## lnblack 0.111498594865494 0.3654445564 0.8042019913
## lnhispanic 0.979373499399558 0.3160523131 0.3771322255
## lnuninsured 0.834862695500020 0.9252225047 0.8816482836
## lnincome_ratio 0.883363530964298 0.1590532401 0.2462620890
## lnteenbirth 0.003300226077460 0.0350135726 0.0104169963
## lnunmarried 0.034877348778877 0.0004571019 0.0004917500Significant impacts include lnretail, lnmanufacturing, urban, retail, lnag, lnunmarried,lnteenbirth. Spatial Durbin Error Model may be most appropriate?
LR.Sarlm(sd.err,sp.err.model)##
## Likelihood ratio for spatial linear models
##
## data:
## Likelihood ratio = 44.556, df = 15, p-value = 0.00008994
## sample estimates:
## Log likelihood of sd.err Log likelihood of sp.err.model
## 86.0926 63.8144P=.00008994, reject null, do not restrict model, Spatial error durbin model is appropriate.
K-Nearest Neighbor Analysis: Distance Lag Model
summary(all.dist.lag.k1, Nagelkerke = TRUE)##
## Call:
## spatialreg::lagsarlm(formula = equation, data = fl_pov, listw = all.dist.neighb.k1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.2120059 -0.0617265 -0.0079057 0.0386980 0.2862156
##
## Type: lag
## Coefficients: (asymptotic standard errors)
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -1.437645 0.566918 -2.5359 0.0112159
## rural 0.107417 0.222051 0.4837 0.6285658
## urban 0.085909 0.045046 1.9071 0.0565062
## lnmanufacturing 0.093187 0.029804 3.1267 0.0017679
## lnag 0.035180 0.019885 1.7692 0.0768628
## lnretail 0.277058 0.069326 3.9965 0.0000643
## lnhealthss 0.336913 0.093310 3.6107 0.0003054
## lnconstruction 0.078225 0.057859 1.3520 0.1763788
## lnlesshs 0.193254 0.070116 2.7562 0.0058481
## lnsinglemom -0.047369 0.066330 -0.7141 0.4751433
## lnblack 0.014666 0.031047 0.4724 0.6366472
## lnhispanic 0.040376 0.035075 1.1511 0.2496752
## lnuninsured 0.067136 0.162385 0.4134 0.6792842
## lnincome_ratio -0.116513 0.130013 -0.8962 0.3701637
## lnteenbirth 0.038407 0.034011 1.1293 0.2587799
## lnunmarried 0.080346 0.052957 1.5172 0.1292180
##
## Rho: 0.15037, LR test value: 1.7448, p-value: 0.18653
## Asymptotic standard error: 0.11649
## z-value: 1.2909, p-value: 0.19675
## Wald statistic: 1.6663, p-value: 0.19675
##
## Log likelihood: 61.32609 for lag model
## ML residual variance (sigma squared): 0.0093165, (sigma: 0.096522)
## Nagelkerke pseudo-R-squared: 0.67447
## Number of observations: 67
## Number of parameters estimated: 18
## AIC: -86.652, (AIC for lm: -86.907)
## LM test for residual autocorrelation
## test value: 0.049768, p-value: 0.82347K-Nearest Neighbor Analysis: Distance Error Model
summary(all.dist.err.k1, Nagelkerke = TRUE)##
## Call:
## spatialreg::errorsarlm(formula = equation, data = fl_pov, listw = all.dist.neighb.k1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.2269206 -0.0587658 -0.0047593 0.0470413 0.2687581
##
## Type: error
## Coefficients: (asymptotic standard errors)
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -1.252963 0.531852 -2.3558 0.0184804
## rural -0.133576 0.218750 -0.6106 0.5414430
## urban 0.040883 0.042232 0.9681 0.3330071
## lnmanufacturing 0.087987 0.029736 2.9590 0.0030867
## lnag 0.019652 0.021507 0.9137 0.3608599
## lnretail 0.274675 0.064526 4.2568 0.00002073
## lnhealthss 0.365105 0.092468 3.9484 0.00007866
## lnconstruction 0.065419 0.054189 1.2072 0.2273429
## lnlesshs 0.234528 0.064005 3.6642 0.0002481
## lnsinglemom -0.080518 0.063750 -1.2630 0.2065774
## lnblack 0.027206 0.028823 0.9439 0.3452196
## lnhispanic 0.037424 0.037056 1.0099 0.3125329
## lnuninsured 0.138577 0.160576 0.8630 0.3881381
## lnincome_ratio -0.065958 0.120856 -0.5458 0.5852323
## lnteenbirth 0.032470 0.031173 1.0416 0.2975875
## lnunmarried 0.018863 0.050774 0.3715 0.7102604
##
## Lambda: 0.39437, LR test value: 3.5368, p-value: 0.060023
## Asymptotic standard error: 0.12098
## z-value: 3.2596, p-value: 0.0011155
## Wald statistic: 10.625, p-value: 0.0011155
##
## Log likelihood: 62.22206 for error model
## ML residual variance (sigma squared): 0.0086472, (sigma: 0.09299)
## Nagelkerke pseudo-R-squared: 0.68306
## Number of observations: 67
## Number of parameters estimated: 18
## AIC: NA (not available for weighted model), (AIC for lm: -86.907)Comparing Models
Distance Lag Model R^2=0.67447 P=0.18653 AIC=-86.652
Distance Error Model R^2=0.68306 P=0.060023 AIC=-88.444
Distance error model is better fit than distance lag model
AIC Values of Best Models
AIC(SLX.model)## [1] -102.7973AIC(sd.err)## [1] -106.1852AIC(all.dist.err.k1)## [1] -88.44413The best model appears to be the spatial durbin error model, with an AIC value of -106.1852. The second best model is the Spatially lagged X model, with an AIC value of -102.7973. The third best model is the distance error model.
Mapping Results
I will use the spatial durbin error model for my map since it had the smallest AIC value of the top three models I tested.
dist.err.data <- summary(sd.err, correlation=TRUE, Nagelkerke = TRUE)
dist.err.output <- cbind.data.frame(fl_pov$FIPS,
dist.err.data$fitted.values,
dist.err.data$residual,
fl_pov$child.pov.2016,
fl_pov$lnsinglemom,
fl_pov$lnuninsured,
fl_pov$lnlesshs,
fl_pov$lnincome_ratio,
fl_pov$lnteenbirth,
fl_pov$lnunemployment,
fl_pov$lnhealthss,
stringsAsFactors = FALSE)
#Renaming columns
colnames(dist.err.output) <- c("fips","fitted","resid","childpov",
"single_mom","uninsured","less_hs","income_ratio","Teen_births","Unemployment","lnhealthss")
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